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CATEGORIES:Optimisation and Numerical Analysis Seminars
SUMMARY:Optimisation over the efficient set of a multi-obj
ective optimisation problem - Zhengliang Liu (Scho
ol of Mathematics\, University of Birmingham)
DTSTART:20171005T110000Z
DTEND:20171005T120000Z
UID:TALK2908AT
URL:/talk/index/2908
DESCRIPTION:Optimisation over the efficient set of a multi-obj
ective optimisation problem is a mathematical mode
l for the problem of selecting a most preferred so
lution that arises in multiple criteria decision m
aking to account for trade-offs between objectives
within the set of efficient solutions. In this st
udy we consider a particular case of this problem\
, namely that of optimising a linear function over
the image of the efficient set in objective space
of a convex multi-objective optimisation problem.
We present both primal and dual algorithms for th
is task. The algorithms are based on recent algori
thms for solving convex multi-objective optimisati
on problems in objective space with suitable modif
ications to exploit specific properties of the pro
blem of optimisation over the efficient set. We fi
rst present the algorithms for the case that the u
nderlying problem is a multi-objective linear prog
ramme. We then extend them to be able to solve pro
blems with an underlying convex multi-objective op
timisation problem. We compare the new algorithms
with several state of the art algorithms from the
literature on a set of randomly generated instance
s to demonstrate that they are considerably faster
than the competitors.\n\nWe then apply the primal
and dual algorithms to compute the nadir point of
a multi-objective linear programme. The nadir poi
nt is the vector consisting of the worst values th
e individual objective functions attain over the n
on-dominated set of the multi-objective linear pro
gramme. Its knowledge is important for multiple cr
iteria decision making\, but its exact determinati
on is difficult\, hence few exact algorithms to co
mpute it exist. We compare the performance of the
primal and dual algorithms to the two known exact
methods from the literature\, namely the algorithm
of Ehrgott and Tenfelde-Podehl (2003) and the alg
orithm of Alves and Costa (2009). It turns out tha
t the dimension reduction in the algorithm of Ehrg
ott and Tenfelde-Podehl is the decisive factor in
this comparison and explains its superior performa
nce.\n\n
LOCATION:G13\, Arts Building
CONTACT:Sergey Sergeev
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